Higher order chromatin structure in eukaryotes can lead to differential gene expression in response to the same transcription factor; however, how transcription factor inputs integrate with quantitative features of the chromatin environment to regulate gene expression is not clear. In vitro models of HIV gene regulation, in which repressive mechanisms acting locally at an integration site keep proviruses transcriptionally silent until appropriately stimulated, provide a powerful system to study gene expression regulation in different chromatin environments. Here we quantified HIV expression as a function of activating transcription factor nuclear factor-κB RelA/p65 (RelA) levels and chromatin features at a panel of viral integration sites. Variable RelA overexpression demonstrated that the viral genomic location sets a threshold RelA level necessary to induce gene expression. However, once the induction threshold is reached, gene expression increases similarly for all integration sites. Furthermore, we found that higher induction thresholds are associated with repressive histone marks and a decreased sensitivity to nuclease digestion at the LTR promoter. Increasing chromatin accessibility via inhibition of histone deacetylation or DNA methylation lowered the induction threshold, demonstrating that chromatin accessibility sets the level of RelA required to activate gene expression. Finally, a functional relationship between gene expression, RelA level, and chromatin accessibility accurately predicted synergistic HIV activation in response to combinatorial pharmacological perturbations. Different genomic environments thus set a threshold for transcription factor activation of a key viral promoter, which may point toward biological principles that underlie selective gene expression and inform strategies for combinatorial therapies to combat latent HIV.